Packing d-degenerate graphs

Authors:
Béla Bollobás;Alexandr Kostochka;Kittikorn Nakprasit
Affiliations:
University of Memphis, Memphis, TN 38152, USA and Trinity College, Cambridge CB2 1TQ, England, UK;University of Illinois, Urbana, IL 61801, USA and Institute of Mathematics, Novosibirsk 630090, Russia;University of Illinois, Urbana, IL 61801, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

Citing 4
Cited 2

2-factors in dense graphs

Discrete Mathematics
Proof of a Conjecture of Bollobás and Eldridge for Graphs of Maximum Degree Three

Combinatorica
On Equitable Coloring of d-Degenerate Graphs

SIAM Journal on Discrete Mathematics
On Two Conjectures on Packing of Graphs

Combinatorics, Probability and Computing

Note: Packing of graphs with small product of sizes

Journal of Combinatorial Theory Series B
Embedding into Bipartite Graphs

SIAM Journal on Discrete Mathematics

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Abstract

We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) Bollobas-Eldridge-Catlin Conjecture holds in a considerably stronger form if one of the graphs is d-degenerate for d not too large: if d,@D"1,@D"2=1 and nmax{40@D"1ln@D"2,40d@D"2} then a d-degenerate graph of maximal degree @D"1 and a graph of order n and maximal degree @D"2 pack. We use this result to show that, for d fixed and n large enough, one can pack n1500d^2 arbitrary d-degenerate n-vertex graphs of maximal degree at most n1000dlnn.